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# Growing by Powers of Ten

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Students will be able to describe what happens to the size of a number as it is multiplied by powers of 10. Students will be able to explain patterns in the number of zeros of the product when multiplying by powers of 10.

(5 minutes)
• To begin the lesson, activate students' prior knowledge by using base ten blocks to review powers of 10.
• With the blocks, show a unit and ask what the value is. Write 1 on the board.
• Show a rod and ask what the value is. Write 10 on the board.
• Then, show a flat and ask what the value is. Write 100 on the board.
• Last, show a cube and ask what the value is. Write 1000 on the board.
• Ask students what would come after 1000. Write 10,000 on the board.
• If appropriate for your students, go to 100,000 and 1,000,000.
• Keep all of the numbers you wrote on the board for the next part of the lesson.
(15 minutes)
• Now, explain to students that the numbers on the board represent powers of ten.
• Pass out the Growing by Powers of Ten Chart.
• Tell students that they are going to work together to fill in the chart, which will then be used to help them solve powers of ten multiplication problems.
• Go over each column heading for the chart. Either display the chart on the whiteboard or make an anchor chart with the same chart.
• Ask students if they know what an exponent is. Explain that an exponent is a shorthand way to tell how many times to use a number in multiplication problems.
• Talk through filling the chart, one row at a time.
• Once the chart is filled in, ask students what patterns they notice.
• Make sure students understand that each power represents an increase of 10 times the number.
(5 minutes)
• Tell students that they will now use the chart to help solve a set of problems involving multiplying by powers of ten.
• Write 3 x 10 to the one power on the board. Explain that because it is 10 to the one power, the problem is still 3 x 10.
• Ask students for the answer. Write 30 on the board.
• Continue modeling by writing: 3 x 10 to the 2 power = 300. 3 x 10 to the 3 power = 3000. 3 x 10 to the fourth power = 30,000. 3 x 10 to the fifth power = 300,000. 3 x 10 to the sixth power = 3,000,000.
• Once you have reached 3,000,000, stop and ask students what happened as they multiplied by another power of ten. Make sure they understand that the answers grew by zero, and that represents a power of ten.
(25 minutes)
• Tell students that the goal of this lesson is to understand powers of ten with whole numbers, and in future lessons, they will understand powers of ten with relation to decimals.
• Pass out the Growing by Powers of Ten Practice Problems worksheet.
• Instruct your students to use their Growing by Powers of Ten Chart and base ten blocks as needed to help them solve the practice problems.
• As students work, walk around the room to provide help to students who need extra support.
• Enrichment: Give your students the Growing by Powers of Ten Challenge Problems to complete. Depending on how advanced they are, you may also have them complete the Growing by Powers of Ten Chart on their own or paired with another advanced student.
• Support: Give your students base ten blocks to use in the chart. Have them draw a picture if they need more visuals of the multiplication problems.
(10 minutes)
• As your students are completing the chart and worksheets, make sure that they are understanding the purpose of exponents.
• Walk around, and informally assess their understanding, scaffolding their learning where needed with blocks and visuals.
• Pick up their worksheets at the end of the class to check for understanding.
(5 minutes)
• Gather your students together for a quick review. Write a few multiplication problems on the board.
• Ask students to help solve them, and encourage them to explain their reasoning and write out the extended number.

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